- 2203/22/2023
Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Synchronization in a Kuramoto Mean Field Game
CMSA, 20 Garden Street, Cambridge, MA 02138 USASpeaker: Mete Soner (Princeton University)
Title: Synchronization in a Kuramoto Mean Field Game
Abstract: Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from incoherence to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.
Some rigorous results on the Lévy spin glass model
Probability Seminar
Speaker: Wei-Kuo Chen (Minnesota)Title: Some rigorous results on the Lévy spin glass model
Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.
- 2203/22/2023
Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Synchronization in a Kuramoto Mean Field Game
CMSA, 20 Garden Street, Cambridge, MA 02138 USASpeaker: Mete Soner (Princeton University)
Title: Synchronization in a Kuramoto Mean Field Game
Abstract: Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from incoherence to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.
Some rigorous results on the Lévy spin glass model
Probability Seminar
Speaker: Wei-Kuo Chen (Minnesota)Title: Some rigorous results on the Lévy spin glass model
Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.
- 2203/22/2023
Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Synchronization in a Kuramoto Mean Field Game
CMSA, 20 Garden Street, Cambridge, MA 02138 USASpeaker: Mete Soner (Princeton University)
Title: Synchronization in a Kuramoto Mean Field Game
Abstract: Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from incoherence to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.
Some rigorous results on the Lévy spin glass model
Probability Seminar
Speaker: Wei-Kuo Chen (Minnesota)Title: Some rigorous results on the Lévy spin glass model
Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.
- 2203/22/2023
Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Synchronization in a Kuramoto Mean Field Game
CMSA, 20 Garden Street, Cambridge, MA 02138 USASpeaker: Mete Soner (Princeton University)
Title: Synchronization in a Kuramoto Mean Field Game
Abstract: Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from incoherence to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.
Some rigorous results on the Lévy spin glass model
Probability Seminar
Speaker: Wei-Kuo Chen (Minnesota)Title: Some rigorous results on the Lévy spin glass model
Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.
- 2203/22/2023
Math Science Lectures in Honor of Raoul Bott: Michael Freedman
On October 4th and October 5th, 2021, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom.This will be the third annual lecture series held in honor of Raoul Bott.
Lecture 1
October 4th, 11:00am (Boston time)Title: The Universe from a single Particle Abstract: I will explore a toy model for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709.
Lecture 2
October 5th, 11:00am (Boston time)Title: Controlled Mather Thurston Theorems. Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374
Synchronization in a Kuramoto Mean Field Game
CMSA, 20 Garden Street, Cambridge, MA 02138 USASpeaker: Mete Soner (Princeton University)
Title: Synchronization in a Kuramoto Mean Field Game
Abstract: Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from incoherence to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.
Some rigorous results on the Lévy spin glass model
Probability Seminar
Speaker: Wei-Kuo Chen (Minnesota)Title: Some rigorous results on the Lévy spin glass model
Abstract: The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.